Defending Graph Neural Networks Against Adversarial attacks via Symmetric Matrix Factorization

Graph neural networks (GNNs) have demonstrated broad applicability across various domains such as social and biological networks. However, their susceptibility to noise and adversarial attacks in input data poses a significant challenge. Even subtle perturbations within graphs can lead to notable performance deterioration, highlighting the importance of enhancing GNN robustness against such challenges. Current defense methods for GNNs often suffer from computational inefficiency and lack scalability. Recent research has revealed that attacked graph models often exhibit violations of the lowrank property. In this paper, we propose a framework for enhancing the robustness of GNNs using non-negative matrix factorization. Our approach involves decomposing the adjacency matrix into two low-rank matrices, effectively capturing the underlying graph structure while mitigating noise. Our method operates in two stages: in the first stage, low-rank matrices are optimized by solving a non-convex matrix factorization problem. Subsequently, a GNN model is trained using this refined graph representation. While we demonstrate our approach using the graph convolutional neural network (GCN) architecture in our experiments, our proposed framework is adaptable to various existing GNN architectures. Simulation results on benchmark datasets validate the effectiveness of our proposed method.